To find the slant height of a cone, you can use the Pythagorean theorem, relating the radius, height, and slant height of the cone.
Understanding the Relationship
The slant height (l), the radius (r), and the height (h) of a right cone form a right triangle, with the slant height being the hypotenuse. Therefore, the Pythagorean theorem applies:
- a² + b² = c² becomes r² + h² = l²
Steps to Calculate Slant Height
- Identify the radius (r) and height (h) of the cone. These values must be known or calculable.
- Apply the Pythagorean theorem: l = √(r² + h²)
- Substitute the values of r and h into the formula.
- Calculate the result to find the slant height (l).
Example
Let's say a cone has a radius of 3 units and a height of 6 units. To find the slant height:
- r = 3
- h = 6
- l = √(3² + 6²)
- l = √(9 + 36)
- l = √45
- l ≈ 6.71 units
Therefore, the slant height of the cone is approximately 6.71 units.
